Can you tell me why the exact 95% confidence interval brackets 1 while the P
value is < .05?

In a logistic regression I was suspicious of the rather narrow confidence
intervals in the analysis of a relatively rare event so I checked using a
2x2 table with an exact test (results below) and the exact confidence
interval does indeed bracket 1, but the p-value given is less than .05(?).

Can you tell me how to interpret/report this?

The distribution of a statistic assuming the null to be true, which
is used to obtain a p-value, is not the same as the distribution of a
statistic when the null is not assumed to be true, as is the case for
a confidence interval. The formulae for ordinary asymptotic tests for
means, for example, obscure this fact, but a simple demonstration of
the principle can be seen in the formula for the standard error for
the test on a single proportion, vs. the standard error expression in
the formula for a confidence interval on a proportion: The form is
the same, but one formula uses an assumed null value, while the other
uses an observed value, which are in general quite different. The
practice of using confidence intervals as a closet hypothesis test is
essentially a trick that happens to work only with statistics for
which the distribution is the same whether or not the null is
true. The resolution of the chimerical contradiction, then, is to
not intepret your CI as though it were a slightly disguised
hypothesis test. It rests on a different logic and answers a
different question.